Write the truth table for the circuit shown in Fig. Name the gate so formed.

Explanation

Here gates I, II and III are NOR, NAND and AND gates respectively.
Output of gate I, `y_(1)=bar(A+B)`
Output of gate II, `y_(2)=bar(A.B)`
Output of gate III,
`y=y_(1).y_(2)=bar((A+B)).bar((A.B))`
`y = y_(2).y_(2) = (bar(A+B)).(bar(A.B))`
`=(barA.barB) .(barA.barB) = bar(A). (barA.barB) +bar(B).(bar(A).bar(B))`
`=bar(A).bar(A).bar(B) +bar(B).bar(A.)bar(B) = bar(A).bar(B) +bar(A).bar(B)`
`=bar(A).bar(B) =bar(A+B)`
`[ :' bar(A).bar(A)=bar(A) and bar(B).bar(B) = bar(B)]`
Thus NOR gate is obtained
The truth table of this logic circuit is given below.
`|{:(A,B,(A+B),(A.B),(bar(A+B)),(bar(A.B)),y=(bar(A+B)).(bar(A.B))),(0,0,0,0,1,1,1),(0,1,1,0,0,1,0),(0,1,1,0,0,1,0),(1,1,1,1,0,0,0):}:|`